In this paper,we propose a parameterization transfer algorithm for planar domains bounded by B-spline curves,where the shapes of the planar domains are similar.The domain geometries are considered to be similar if the...In this paper,we propose a parameterization transfer algorithm for planar domains bounded by B-spline curves,where the shapes of the planar domains are similar.The domain geometries are considered to be similar if their simplified skeletons have the same structures.One domain we call source domain,and it is parameterized using multi-patch B-spline surfaces.The resulting parameterization is C1 continuous in the regular region and G1 continuous around singular points regardless of whether the parameterization of the source domain is C1/G1 continuous or not.In this algorithm,boundary control points of the source domain are extracted from its parameterization as sequential points,and we establish a correspondence between sequential boundary control points of the source domain and the target boundary through discrete sampling and fitting.Transfer of the parametrization satisfies C1/G1 continuity under discrete harmonic mapping with continuous constraints.The new algorithm has a lower calculation cost than a decomposition-based parameterization with a high-quality parameterization result.We demonstrate that the result of the parameterization transfer in this paper can be applied in isogeometric analysis.Moreover,because of the consistency of the parameterization for the two models,this method can be applied in many other geometry processing algorithms,such as morphing and deformation.展开更多
The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by a...The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.62072148 and U22A2033)the National Key R&D Program of China(Grant Nos.2022YFB3303000 and 2020YFB1709402)+2 种基金the Zhejiang Provincial Science and Technology Program in China(Grant No.2021C01108)the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization(Grant No.U1909210)the Fundamental Research Funds for the Provincial Universities of Zhejiang(Grant No.490 GK219909299001-028).
文摘In this paper,we propose a parameterization transfer algorithm for planar domains bounded by B-spline curves,where the shapes of the planar domains are similar.The domain geometries are considered to be similar if their simplified skeletons have the same structures.One domain we call source domain,and it is parameterized using multi-patch B-spline surfaces.The resulting parameterization is C1 continuous in the regular region and G1 continuous around singular points regardless of whether the parameterization of the source domain is C1/G1 continuous or not.In this algorithm,boundary control points of the source domain are extracted from its parameterization as sequential points,and we establish a correspondence between sequential boundary control points of the source domain and the target boundary through discrete sampling and fitting.Transfer of the parametrization satisfies C1/G1 continuity under discrete harmonic mapping with continuous constraints.The new algorithm has a lower calculation cost than a decomposition-based parameterization with a high-quality parameterization result.We demonstrate that the result of the parameterization transfer in this paper can be applied in isogeometric analysis.Moreover,because of the consistency of the parameterization for the two models,this method can be applied in many other geometry processing algorithms,such as morphing and deformation.
基金supported by the National Natural Science Foundation of China (Grant Nos.51178247 and 50778104)the National High Technology Research and Development Program of China (Grant No.2009AA04Z401)
文摘The recently proposed weak form quadrature element method （QEM） is applied to flexural and vibrational analysis of thin plates The integrals involved in the variational description of a thin plate are evaluated by an efficient numerical scheme and the par- tial derivatives at the integration sampling points are then approximated using differential quadrature analogs. Neither the grid pattern nor the number of nodes is fixed, being adjustable according to convergence need. The C~ continuity conditions char- acterizing the thin plate theory are discussed and the robustness of the weak form quadrature element for thin plates against shape distortion is examined. Examples are presented and comparisons with analytical solutions and the results of the finite element method are made to demonstrate the convergence and computational efficiency of the weak form quadrature element method. It is shown that the present formulation is applicable to thin plates with varying thickness as well as uniform plates.
